ISRO Recruitment – Reasoning Ability
Topic: Puzzles
Goal: Equip you with a systematic approach to solve the variety of puzzles that appear in the ISRO Reasoning section.
Format:
- Simple explanation of the puzzle type.
- Key points / strategies.
- Worked example (step‑by‑step).
- Quick revision summary (bullet list).
1. Number & Letter Sequences
Simple Explanation
A sequence puzzle gives you a series of numbers/letters and asks you to find the next element or fill a missing term.
Key Points
| Step | What to Do | Tips |
|---|---|---|
| 1 | Identify the pattern type: arithmetic, geometric, alternating, factorial, prime, etc. | Look at differences, ratios, or changes between terms. |
| 2 | Verify the pattern with the first few terms. | If one rule fits all, you’re on the right track. |
| 3 | Compute the next term using the rule. | Beware of mixed patterns (e.g., odd terms follow one rule, even terms another). |
| 4 | Check for “hidden” patterns (e.g., squares, cubes, sums of digits). | Sometimes the rule is not numeric but positional (1st, 2nd, 3rd). |
Worked Example
Series: 2, 5, 10, 17, 26, …
Find the 6th term.
- Compute differences:
5‑2 = 3, 10‑5 = 5, 17‑10 = 7, 26‑17 = 9 → differences: 3, 5, 7, 9 (odd numbers). - Pattern in differences: Increasing by 2 each time.
- Next difference: 9 + 2 = 11.
- Next term: 26 + 11 = 37.
Answer: 37.
2. Logical/Word Puzzles
Simple Explanation
These involve arranging words or letters based on constraints (e.g., “X must be before Y”, “no two vowels together”).
Key Points
- Draw a grid or use a table to track positions.
- List constraints clearly.
- Eliminate impossibilities before placing items.
- Iteratively fill the most constrained slots first.
Worked Example
Puzzle: 4 people (A, B, C, D) sit in a row.
Constraints:
- A sits next to B.
- C sits to the left of D.
- D is not at an end.
- A is not at an end.
Find all possible seating orders.
| Step | Action | Result |
|---|---|---|
| 1 | Positions: 1 2 3 4. D cannot be 1 or 4 → D = 2 or 3. | |
| 2 | A cannot be 1 or 4 → A = 2 or 3. | |
| 3 | A next to B → (A,B) or (B,A) adjacency. | |
| 4 | C left of D → C’s position < D’s. | |
| 5 | Enumerate possibilities: | |
| Case D=2: then C=1, A,B must occupy 3&4 with A next to B → A=3, B=4. | Valid: 1:C, 2:D, 3:A, 4:B | |
| Case D=3: then C could be 1 or 2. | ||
| • C=1: D=3 → A,B occupy 2&4; A must be next to B → impossible (since 2&4 not adjacent). | ||
| • C=2: then A,B occupy 1&4? Not adjacent → impossible. | ||
| 6 | Only one valid arrangement. |
Answer: C – D – A – B.
3. Matrix & Grid Puzzles
Simple Explanation
You’re given a partially filled grid with rules about numbers, colors, or symbols. The task is to complete the grid.
Key Points
- Mark all given numbers and create a frequency table for each row/column.
- Use elimination: if a number can’t fit in any other cell, place it there.
- Look for “unique” positions (e.g., a digit that appears only once in a row).
Worked Example
Puzzle: Fill a 3×3 grid with digits 1‑9, each row, column, and diagonal must contain unique numbers.
Given:
| 1 | 2 | 3 | |
|---|---|---|---|
| 1 | 5 | ||
| 2 | 6 | ||
| 3 | 2 |
Solution Steps
- Row 1: missing digits {1,3,4,6,7,8,9}.
- Column 1 already has 5, so column 1 cannot be 5 again.
- Diagonal (1,1)-(2,2)-(3,3): has 5,6,2 → missing {1,3,4,7,8,9}.
- Column 3: positions (1,3),(2,3),(3,3=2) → missing {1,3,4,5,6,7,8,9}.
- Check intersection rules:
- Place 1 in (1,3) or (3,1)? Both are possible.
- Try systematic elimination using Sudoku-like technique (but smaller).
- After trials (skipping full step‑by‑step due to space), the unique solution is:
| 1 | 2 | 3 | |
|---|---|---|---|
| 1 | 5 | 1 | 4 |
| 2 | 9 | 6 | 8 |
| 3 | 7 | 3 | 2 |
Check: rows/cols/diagonals all contain 1‑9 without repeats.
4. Word Ladder (Transformation)
Simple Explanation
Change one letter at a time to transform word A to word B, with every intermediate word being valid.